Least Common Multiple (LCM) of 110 and 118
The least common multiple (LCM) of 110 and 118 is 6490.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 110 and 118?
First, calculate the GCD of 110 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 118 = 0 remainder 110 |
| 2 | 118 ÷ 110 = 1 remainder 8 |
| 3 | 110 ÷ 8 = 13 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 70 | 13930 |
| 112 and 190 | 10640 |
| 159 and 172 | 27348 |
| 80 and 70 | 560 |
| 105 and 62 | 6510 |